Computing the characteristic polynomials of a class of hyperelliptic curves for cryptographic applications
type: Item
instance of: scholarly article
title: Computing the characteristic polynomials of a class of hyperelliptic curves for cryptographic applications
zbMATH Open document ID: 1213.94144
DOI: 10.1155/2011/437541
author: Lin You
author: Guangguo Han
author: Yongxuan Sang
author: Jiwen Zeng
published in: Mathematical Problems in Engineering
publication date: 2011-06-07T00:00:00Z
full work available at URL: https://eudml.org/doc/223750
review text: Summary: Hyperelliptic curves have been widely studied for cryptographic applications, and some special hyperelliptic curves are often considered to be used in practical cryptosystems. Computing Jacobian group orders is an important operation in constructing hyperelliptic curve cryptosystems, and the most common method used for the computation of Jacobian group orders is by computing the zeta functions or the characteristic polynomials of the related hyperelliptic curves. For the hyperelliptic curve \(C_q:v^2 = u^p + au + b\) over the field \(\mathbb{F}_q\) with \(q\) being a power of an odd prime \(p\), Duursma and Sakurai obtained its characteristic polynomial for \(q = p\), \(a = -1\), and \(b \in \mathbb{F}_p\). In this paper, we determine the characteristic polynomials of \(C_q\) over the finite field \(\mathbb{F}_{p^n}\) for \(n = 1, 2\) and \(a, b \in \mathbb{F}_{p^n}\). We also give some computational data which show that many of those curves have large prime factors in their Jacobian group orders, which are both practical and vital for the constructions of efficient and secure hyperelliptic curve cryptosystems.
Mathematics Subject Classification ID: 94A60
Mathematics Subject Classification ID: 14G50
zbMATH DE Number: 5904893
describes a project that uses: HECC
MaRDI profile type: Publication
OpenAlex ID: W2038210060
Wikidata QID: Q58693051
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description: scientific article; zbMATH DE number 5904893